Answer :
To determine the operation that relates the number of carnival tickets sold to the dollars donated, we can analyze the given table:
[tex]\[ \begin{tabular}{|c|c|} \hline Tickets sold & Dollars donated \\ \hline 10 & 5 \\ \hline 20 & 10 \\ \hline 30 & 15 \\ \hline 40 & 20 \\ \hline 50 & 25 \\ \hline \end{tabular} \][/tex]
We observe the pairs of values:
1. When 10 tickets are sold, \[tex]$5 are donated. 2. When 20 tickets are sold, \$[/tex]10 are donated.
3. When 30 tickets are sold, \[tex]$15 are donated. 4. When 40 tickets are sold, \$[/tex]20 are donated.
5. When 50 tickets are sold, \$25 are donated.
To identify the operation, let's consider different candidate operations:
1. Add 2:
[tex]\[ \begin{align*} 10 + 2 &= 12 \quad (\text{not equal to 5}) \\ 20 + 2 &= 22 \quad (\text{not equal to 10}) \\ 30 + 2 &= 32 \quad (\text{not equal to 15}) \\ 40 + 2 &= 42 \quad (\text{not equal to 20}) \\ 50 + 2 &= 52 \quad (\text{not equal to 25}) \\ \end{align*} \][/tex]
Clearly, adding 2 does not match the corresponding dollars donated.
2. Multiply by 2:
[tex]\[ \begin{align*} 10 \times 2 &= 20 \quad (\text{not equal to 5}) \\ 20 \times 2 &= 40 \quad (\text{not equal to 10}) \\ 30 \times 2 &= 60 \quad (\text{not equal to 15}) \\ 40 \times 2 &= 80 \quad (\text{not equal to 20}) \\ 50 \times 2 &= 100 \quad (\text{not equal to 25}) \\ \end{align*} \][/tex]
Clearly, multiplying by 2 does not match the corresponding dollars donated either.
3. Subtract 2:
[tex]\[ \begin{align*} 10 - 2 &= 8 \quad (\text{not equal to 5}) \\ 20 - 2 &= 18 \quad (\text{not equal to 10}) \\ 30 - 2 &= 28 \quad (\text{not equal to 15}) \\ 40 - 2 &= 38 \quad (\text{not equal to 20}) \\ 50 - 2 &= 48 \quad (\text{not equal to 25}) \\ \end{align*} \][/tex]
Clearly, subtracting 2 does not match the corresponding dollars donated.
4. Divide by 2:
[tex]\[ \begin{align*} 10 \div 2 &= 5 \\ 20 \div 2 &= 10 \\ 30 \div 2 &= 15 \\ 40 \div 2 &= 20 \\ 50 \div 2 &= 25 \\ \end{align*} \][/tex]
Dividing each number of tickets sold by 2 perfectly matches the number of dollars donated in each case.
Thus, the operation that can be applied to the number of tickets sold to find the number of dollars donated is to divide by 2.
[tex]\[ \begin{tabular}{|c|c|} \hline Tickets sold & Dollars donated \\ \hline 10 & 5 \\ \hline 20 & 10 \\ \hline 30 & 15 \\ \hline 40 & 20 \\ \hline 50 & 25 \\ \hline \end{tabular} \][/tex]
We observe the pairs of values:
1. When 10 tickets are sold, \[tex]$5 are donated. 2. When 20 tickets are sold, \$[/tex]10 are donated.
3. When 30 tickets are sold, \[tex]$15 are donated. 4. When 40 tickets are sold, \$[/tex]20 are donated.
5. When 50 tickets are sold, \$25 are donated.
To identify the operation, let's consider different candidate operations:
1. Add 2:
[tex]\[ \begin{align*} 10 + 2 &= 12 \quad (\text{not equal to 5}) \\ 20 + 2 &= 22 \quad (\text{not equal to 10}) \\ 30 + 2 &= 32 \quad (\text{not equal to 15}) \\ 40 + 2 &= 42 \quad (\text{not equal to 20}) \\ 50 + 2 &= 52 \quad (\text{not equal to 25}) \\ \end{align*} \][/tex]
Clearly, adding 2 does not match the corresponding dollars donated.
2. Multiply by 2:
[tex]\[ \begin{align*} 10 \times 2 &= 20 \quad (\text{not equal to 5}) \\ 20 \times 2 &= 40 \quad (\text{not equal to 10}) \\ 30 \times 2 &= 60 \quad (\text{not equal to 15}) \\ 40 \times 2 &= 80 \quad (\text{not equal to 20}) \\ 50 \times 2 &= 100 \quad (\text{not equal to 25}) \\ \end{align*} \][/tex]
Clearly, multiplying by 2 does not match the corresponding dollars donated either.
3. Subtract 2:
[tex]\[ \begin{align*} 10 - 2 &= 8 \quad (\text{not equal to 5}) \\ 20 - 2 &= 18 \quad (\text{not equal to 10}) \\ 30 - 2 &= 28 \quad (\text{not equal to 15}) \\ 40 - 2 &= 38 \quad (\text{not equal to 20}) \\ 50 - 2 &= 48 \quad (\text{not equal to 25}) \\ \end{align*} \][/tex]
Clearly, subtracting 2 does not match the corresponding dollars donated.
4. Divide by 2:
[tex]\[ \begin{align*} 10 \div 2 &= 5 \\ 20 \div 2 &= 10 \\ 30 \div 2 &= 15 \\ 40 \div 2 &= 20 \\ 50 \div 2 &= 25 \\ \end{align*} \][/tex]
Dividing each number of tickets sold by 2 perfectly matches the number of dollars donated in each case.
Thus, the operation that can be applied to the number of tickets sold to find the number of dollars donated is to divide by 2.
